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Cartan’s Connection, Fiber Bundles and Quaternions in Kinematics and Dynamics Calculations

[+] Author Affiliations
Diego Colón

University of São Paulo, São Paulo, Brazil

Paper No. DETC2015-46758, pp. V05CT08A053; 10 pages
doi:10.1115/DETC2015-46758
From:
  • ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5C: 39th Mechanisms and Robotics Conference
  • Boston, Massachusetts, USA, August 2–5, 2015
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5714-4
  • Copyright © 2015 by ASME

abstract

It is used the concept of Cartan’s connection and principal fiber bundles to obtain formulas for kinematics and dynamics calculations for robotic manipulators. A principal fiber bundle is a differentiable manifold formed by a base space B (in this case ℝ3)) plus all possible reference frames attached to a point p ∈ B (that is the fiber Sp). Cartan’s connections are the most general way to represent velocity of frames. In previous works, those ideas were applied to fiber bundles with fibers homomorphic to the Lie group SO(3) (or SE(3)). In this paper, it is applied to the case of fibers homomorphic either to the group SU(2) (for rotational motion) or to the group of unit dual quaternions (for translational plus rotational motion). It is also presented some results of calculations, and indicate future directions for research.

Copyright © 2015 by ASME

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